Problema Solution
a certain mine yields low grade oil shale containing 18.0 gallons of oil per ton of rock and another mine has shale yeilding 30.0 gal/ton.How many tons of each must be sent each day to a processing plant that processes 25,000 tons of rock per day so that the overall yeild will be 23.0 gal/ton.
Answer provided by our tutors
let
x = tones of the low grade oil shale containing 18.0 gallons of oil per ton of rock
y = tones of the other mine that has a shale yielding 30.0 gal/ton
the processing plant processes 25,000 tons of rock per day this means that
x + y = 25000
the yield from x + the yield from y = the overall yield 23.0 gal/ton of 25,000 tons of rock
18*x + 30*y = 23*25000
by solving the system of equations
x + y = 25000
18*x + 30*y = 23*25000
we find
x = 14,583.3 t
y = 10,416.6 t
14,583.3 t of of the low grade oil shale and 10,416.6 t of the other mine should be sent each day to the processing plant.